module Ord  = struct
  type t = int

end
let compare (x : int) (y : int) = compare x y
(* module Make(Ord: OrderedType) = struct *)

type key = Ord.t

type 'a t =
    Empty
  | Node of 'a t * key * 'a * 'a t * int

let height = function
    Empty -> 0
  | Node(_,_,_,_,h) -> h

let create l x d r =
  let hl = height l and hr = height r in
  Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))

let singleton x d = Node(Empty, x, d, Empty, 1)

let bal l x d r =
  let hl = match l with Empty -> 0 | Node(_,_,_,_,h) -> h in
  let hr = match r with Empty -> 0 | Node(_,_,_,_,h) -> h in
  if hl > hr + 2 then begin
    match l with
      Empty -> invalid_arg "Map.bal"
    | Node(ll, lv, ld, lr, _) ->
      if height ll >= height lr then
        create ll lv ld (create lr x d r)
      else begin
        match lr with
          Empty -> invalid_arg "Map.bal"
        | Node(lrl, lrv, lrd, lrr, _)->
          create (create ll lv ld lrl) lrv lrd (create lrr x d r)
      end
  end else if hr > hl + 2 then begin
    match r with
      Empty -> invalid_arg "Map.bal"
    | Node(rl, rv, rd, rr, _) ->
      if height rr >= height rl then
        create (create l x d rl) rv rd rr
      else begin
        match rl with
          Empty -> invalid_arg "Map.bal"
        | Node(rll, rlv, rld, rlr, _) ->
          create (create l x d rll) rlv rld (create rlr rv rd rr)
      end
  end else
    Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))

let empty = Empty

let is_empty = function Empty -> true | _ -> false

let rec add x data = function
    Empty ->
    Node(Empty, x, data, Empty, 1)
  | Node(l, v, d, r, h) ->
    let c = compare x v in
    if c = 0 then
      Node(l, x, data, r, h)
    else if c < 0 then
      bal (add x data l) v d r
    else
      bal l v d (add x data r)

let rec find x = function
    Empty ->
    raise Not_found
  | Node(l, v, d, r, _) ->
    let c = compare x v in
    if c = 0 then d
    else find x (if c < 0 then l else r)

let rec mem x = function
    Empty ->
    false
  | Node(l, v, d, r, _) ->
    let c = compare x v in
    c = 0 || mem x (if c < 0 then l else r)

let rec min_binding = function
    Empty -> raise Not_found
  | Node(Empty, x, d, r, _) -> (x, d)
  | Node(l, x, d, r, _) -> min_binding l

let rec max_binding = function
    Empty -> raise Not_found
  | Node(l, x, d, Empty, _) -> (x, d)
  | Node(l, x, d, r, _) -> max_binding r

let rec remove_min_binding = function
    Empty -> invalid_arg "Map.remove_min_elt"
  | Node(Empty, x, d, r, _) -> r
  | Node(l, x, d, r, _) -> bal (remove_min_binding l) x d r

let merge t1 t2 =
  match (t1, t2) with
    (Empty, t) -> t
  | (t, Empty) -> t
  | (_, _) ->
    let (x, d) = min_binding t2 in
    bal t1 x d (remove_min_binding t2)

let rec remove x = function
    Empty ->
    Empty
  | Node(l, v, d, r, h) ->
    let c = compare x v in
    if c = 0 then
      merge l r
    else if c < 0 then
      bal (remove x l) v d r
    else
      bal l v d (remove x r)

let rec iter f = function
    Empty -> ()
  | Node(l, v, d, r, _) ->
    iter f l; f v d; iter f r

let rec map f = function
    Empty ->
    Empty
  | Node(l, v, d, r, h) ->
    let l' = map f l in
    let d' = f d in
    let r' = map f r in
    Node(l', v, d', r', h)

let rec mapi f = function
    Empty ->
    Empty
  | Node(l, v, d, r, h) ->
    let l' = mapi f l in
    let d' = f v d in
    let r' = mapi f r in
    Node(l', v, d', r', h)

let rec fold f m accu =
  match m with
    Empty -> accu
  | Node(l, v, d, r, _) ->
    fold f r (f v d (fold f l accu))

let rec for_all p = function
    Empty -> true
  | Node(l, v, d, r, _) -> p v d && for_all p l && for_all p r

let rec exists p = function
    Empty -> false
  | Node(l, v, d, r, _) -> p v d || exists p l || exists p r

(* Beware: those two functions assume that the added k is *strictly*
   smaller (or bigger) than all the present keys in the tree; it
   does not test for equality with the current min (or max) key.

   Indeed, they are only used during the "join" operation which
   respects this precondition.
*)

let rec add_min_binding k v = function
  | Empty -> singleton k v
  | Node (l, x, d, r, h) ->
    bal (add_min_binding k v l) x d r

let rec add_max_binding k v = function
  | Empty -> singleton k v
  | Node (l, x, d, r, h) ->
    bal l x d (add_max_binding k v r)

(* Same as create and bal, but no assumptions are made on the
   relative heights of l and r. *)

let rec join l v d r =
  match (l, r) with
    (Empty, _) -> add_min_binding v d r
  | (_, Empty) -> add_max_binding v d l
  | (Node(ll, lv, ld, lr, lh), Node(rl, rv, rd, rr, rh)) ->
    if lh > rh + 2 then bal ll lv ld (join lr v d r) else
    if rh > lh + 2 then bal (join l v d rl) rv rd rr else
      create l v d r

(* Merge two trees l and r into one.
   All elements of l must precede the elements of r.
   No assumption on the heights of l and r. *)

let concat t1 t2 =
  match (t1, t2) with
    (Empty, t) -> t
  | (t, Empty) -> t
  | (_, _) ->
    let (x, d) = min_binding t2 in
    join t1 x d (remove_min_binding t2)

let concat_or_join t1 v d t2 =
  match d with
  | Some d -> join t1 v d t2
  | None -> concat t1 t2

let rec split x = function
    Empty ->
    (Empty, None, Empty)
  | Node(l, v, d, r, _) ->
    let c = compare x v in
    if c = 0 then (l, Some d, r)
    else if c < 0 then
      let (ll, pres, rl) = split x l in (ll, pres, join rl v d r)
    else
      let (lr, pres, rr) = split x r in (join l v d lr, pres, rr)

let rec merge f s1 s2 =
  match (s1, s2) with
    (Empty, Empty) -> Empty
  | (Node (l1, v1, d1, r1, h1), _) when h1 >= height s2 ->
    let (l2, d2, r2) = split v1 s2 in
    concat_or_join (merge f l1 l2) v1 (f v1 (Some d1) d2) (merge f r1 r2)
  | (_, Node (l2, v2, d2, r2, h2)) ->
    let (l1, d1, r1) = split v2 s1 in
    concat_or_join (merge f l1 l2) v2 (f v2 d1 (Some d2)) (merge f r1 r2)
  | _ ->
    assert false

let rec filter p = function
    Empty -> Empty
  | Node(l, v, d, r, _) ->
    (* call [p] in the expected left-to-right order *)
    let l' = filter p l in
    let pvd = p v d in
    let r' = filter p r in
    if pvd then join l' v d r' else concat l' r'

let rec partition p = function
    Empty -> (Empty, Empty)
  | Node(l, v, d, r, _) ->
    (* call [p] in the expected left-to-right order *)
    let (lt, lf) = partition p l in
    let pvd = p v d in
    let (rt, rf) = partition p r in
    if pvd
    then (join lt v d rt, concat lf rf)
    else (concat lt rt, join lf v d rf)

type 'a enumeration = End | More of key * 'a * 'a t * 'a enumeration

let rec cons_enum m e =
  match m with
    Empty -> e
  | Node(l, v, d, r, _) -> cons_enum l (More(v, d, r, e))

let compare cmp m1 m2 =
  let rec compare_aux e1 e2 =
    match (e1, e2) with
      (End, End) -> 0
    | (End, _)  -> -1
    | (_, End) -> 1
    | (More(v1, d1, r1, e1), More(v2, d2, r2, e2)) ->
      let c = compare v1 v2 in
      if c <> 0 then c else
        let c = cmp d1 d2 in
        if c <> 0 then c else
          compare_aux (cons_enum r1 e1) (cons_enum r2 e2)
  in compare_aux (cons_enum m1 End) (cons_enum m2 End)

(* let equal cmp m1 m2 = *)
(*   let rec equal_aux e1 e2 = *)
(*       match (e1, e2) with *)
(*       (End, End) -> true *)
(*     | (End, _)  -> false *)
(*     | (_, End) -> false *)
(*     | (More(v1, d1, r1, e1), More(v2, d2, r2, e2)) -> *)
(*         compare v1 v2 = 0 && cmp d1 d2 && *)
(*         equal_aux (cons_enum r1 e1) (cons_enum r2 e2) *)
(*   in equal_aux (cons_enum m1 End) (cons_enum m2 End) *)

let rec cardinal = function
    Empty -> 0
  | Node(l, _, _, r, _) -> cardinal l + 1 + cardinal r

let rec bindings_aux accu = function
    Empty -> accu
  | Node(l, v, d, r, _) -> bindings_aux ((v, d) :: bindings_aux accu r) l

let bindings s =
  bindings_aux [] s

let choose = min_binding

(* end *)
let m = List.fold_left (fun acc (k,v) -> add k v  acc ) empty [(10,'a'); (3,'b'); (7,'c'); (20,'d') ]

external log : 'a -> unit = "console.log"

;; Mt.from_pair_suites __MODULE__
  [ "find", (fun _ ->
        Mt.Eq  (find 10 m , 'a'))
  ]



